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ELECTROCHEMICAL STUDIES OF SOME METAL ION CRYPTATES IN VARIOUS SOLVENTS By Jila Tabib A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1982 ABSTRACT ELECTROCHEMICAL STUDIES OF SOME METAL ION CRYPTATES IN VARIOUS SOLVENTS By Jila Tabib The Tl(C222)+/Tl(Hg) redox couple was used to determine the thermodynamics of formation of some alkali and alkaline earth C222 cryptates in a number of solvents such as water, dimethylsulfoxide, N,N-dimethylformamide, and methanol, using a competition method. Potassium and thallium cations were uniformly found to exhibit the largest values of stability constants K? in each solvent._ It has been shown that the enthalpic factors contribute a great deal to the stability of alkali and alkaline-earth C222 cryptates, while the values of A83 for most of the cryptates studied here are negative. Cyclic voltammetry was used to monitor the redox chem- istry of the (EuL)3+/2+ (L = 0221, 02 22, and 0222 cryptands), N (YbL)3+/2+(L = 0221 and 0222 cryptands), (SmL)3+/2+(L = 0221 and C222 cryptands), FeC2213+/2+, and (CuL)2+/+(L = 0211, C2Nll, and C2N1N1N cryptands) redox couples in Jila Tabib several solvents such as water, dimethylsulfoxide, N,N- dimethylformamide, N-methylformamide, formamide, prOpylene carbonate and acetonitrile. All of these complexes were substitutionally inert on the cyclic-voltammetric time scale. The substantially lower thermodynamic stabilities of the tri— valent cryptates (compared to the corresponding divalent complexes) arise from large enthalpic destabilizations which outweigh smaller entropic Stabilizations. The higher stabilities of CuII nitrogenated cryptates (CuC2 112+, N 0u02N1N1N2+) with respect to the ordinary cryptate (Cu02112+) are consistent with the expected greater strength of the Cu-N compound to the Cu-O bonds. The influences of the solvent upon the electrode thermo- dynamics of the above redOX'couples have also been studied. The measurements of formal potentials Bf and reaction en- tropies Asgc coupled with extrathermodynamic methods such as the "ferrocene", and "tetraphenylarsonium-tetraphenyl- borate" assumptions, yield estimates of the free energy )S-W, and enthalpy A(AH°)S"W of A(AG°)S'W, entropy A(AS° transfer for the redox couple of interest from water to other solvents. To My Parents 11 ACKNOWLEDGMENTS I would like to express my appreciation to Dr. Michael Weaver for his invaluable advice, guidance, and support during the last four years of my presence at Michigan State University. Thanks are given to Professors A. I. Popov and J. Allison for their helpful suggestions as second readers,and to other members of my Committee, Professors J. Babcock and Ruesch. Special thanks go to Peri-Anne Warstler for her in- valuable typing skill.“ I wish to express sincere thanks to my colleagues in the research group of Dr. Weaver for their assistance in the laboratory, and for their friendship. Finally, I would like to thank my parents and my won- derful husband, Saeed, for their love, understanding, en- couragement and support. 111 TABLE OF CONTENTS Chapter LIST OF TABLES. LIST OF FIGURES . . . . . . INTRODUCTION. . . . . . . . . . . . . . CHAPTER I - HISTORICAL BACKGROUND . A. Introduction. . . . . . . B. Experimental Techniques 1. Electrochemical Techniques. 1.1. Polarography and Cyclic “ ‘”‘ . Voltammetry . . . 1.2. PotentiOmetric Measure- ments . . . . . . . . 1.3. Electrical Conductance Measurements. . . . . . 2. Calorimetric Techniques 3. Spectroscopic Techniques. 3.1. Proton Magnetic Reson- ance (pmr). 3.2. Carbon-13 Magnetic Resonance . . . . 3.3. Nuclear Magnetic Reson- ance of Nuclei Other Than 1H and 130 . . 3.“. Other Spectrosc0pic Techniques. . CHAPTER II - EXPERIMENTAL iv 10 10 10 13 15 l6 l7 l7 l7 18 2M 26 Chapter A. Apparatus B. Electrochemical Techniques. 1. Common Features 2 Cyclic Voltammetry. 3. Preparative Electrolyses. M pH Measurements C. Materials 1. Cryptates 2. Reagents. 3. Solvents. CHAPTER III - THE THALLIUM(I)/THALLIUM AMALGAM COUPLE AS AN ELECTROCHEMICAL PROBE OF CRYPTATE THERMODYNAMICS IN NONAQUEOUS SOLVENTS. A. Introduction. B. Results C. Discussion. 1. Enthalpy and Entropy Contribu- tions to Cryptate Stability 2. Enthalpy and Entropy Contribu- tions to Cryptate Selectivities 3. Solvent Effects on the Thermo- dynamics of Complexation. . CHAPTER IV - TREATMENT OF ELECTROCHEMICAL THERMODYNAMIC DATA FOR COMPLEX- ING REDOX COUPLES . A. Determination of Complexation and Transfer Free Energies. . Page 27 28 28 28 29 29 3O 3O 3O 31 33 3A 3A A8 A8 51 60 65 Chapter Determination of Reaction Entropies for Redox Couples . . . . . . . . CHAPTER V - ELECTROCHEMICAL STUDIES OF SOME TRANSITION METAL ION ‘ CRYPTATES IN VARIOUS SOLVENTS . . . . Introduction. . . . . . . . . . . . . . . . Results . . . . . . . . . . . 1. M(III/II) Cryptate Redox Couples . . . . . . . . . . . . . . . . 1.1. Complexation Thermodynamics . 1.2. Solvent Transfer Thermo- dynamics. . . . . . . . . . . . 2. Cu(II/I) Cryptate Redox Couples . . . 2.1. Complexation Thermodynamics 2.2. Solvent Transfer Thermo- dynamics. . . . . . . . . . . . . ‘Discussion. . . . . . . . . . . . . . . . . 1. The Effect of Varying the Cation Charge and Size Upon Cryptate Thermodynamics. . . . . . . . . . . . . 2. The Effect of Number of Nitrogen Heteroatoms Upon the Thermodynamics of Copper and Europium Cryptates. 3. Effect of Solvent Upon the Thermo- dynamics of M(III)/(II) and M(II)/(I) Transition Metal Cryptate Redox Couples . . . . . . . CHAPTER VI - CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK . . . . . . . . Conclusions . . . . . . . . . . . . . . . l. Alkali and Alkaline Earth Cryptates . . 2. Transition Metal Cryptates. vi Page 72 76 77 78 78 78 98 103 103 105 110 110 113 116 122 123 123 12“ Chapter Page B. Suggestions for Further Work. . . . . . . . 126 REFERENCES. . . . . . . . . . . . . . . . . . . . . 129 vii Table LIST OF TABLES Page Thermodynamics of Mn+C222 Forma- tion in Water at 25°C. . . . . . . . . . . “l Thermodynamics of Mn+0222 Forma- tion in Dimethylsulfoxide at 25°C. . . . . A3 Thermodynamics of Mn+C222 Forma- tion in N,N'-Dimethy1formamide at 25°C. . . . . . . . . . . . . . . . . . uu Thermodynamics of Mn+0222 Forma- ’ tion in Methanol at 25°C . . . . . . . . . A5 Absolute Entropy Differences of K+ and Various Alkali Metal Cations, and the Corresponding Differences of K+0222 and Various Alkali Metal 0222 Cryptates in a Number of Solvents . . . . . . . . . . . . 63 Some Properties of Various Sol- vents. . . . . . . . . . . . c . . . . . . 79 Peak Separations of a Number of Redox Couples in Various Solvents Using 0.1 M TEAP as Supporting Electrolyte at 25°C. . . . . . . . . . . . 8O viii Table 10 11 12 Page Formal Potentials and Reaction 3+/2+, (EuC22l)3+/2+, Entropies for Eu (EuC222)3+/2+, and (Eu02N22)3+/2+ Redox Couples in Various Solvents at 25°C. . . . . . . . . . . . . . . . . 86 Formal Potentials and Entropies of Electron Transfer Reactions of Ytterbium Cryptate Redox Couples in Various Solvents at 25°C (Ionic Strength = 0.1 M) . . . . . . . . 88 Formal Potentials and Entropies of Electron Transfer Reactions of Sm3+/2+, (SmC221)3+/2+, and (Sm0222)3+/2+ Redox Couples in 0.1 M TEAP in Various Solvents at 25°C. . . . . . . . . . . . . . . . . 89 Formal Potentials and Entropies of Electron Transfer Reactions of Fe3+/2+ and (FeC211)3+/2+ Redox Couples in 0.1 M TEAP in Various Solvents at 25°C . . . . . . . . . . . . 9O Thermodynamics of (EuC22l)3+/2+, (Eu0222)3+/2+ )3+/2+ , and (EuC2N22 Redox Couples in Various Sol- vents at 25°C. . . . . . . . . . . . . . 92 ix Table 13 l“ 15 16 17 18 Thermodynamics of Some Ytterbium Cryptate Redox Couples in Various Solvents at 25°C (Ionic Strength = 001M.) 0 o o o o o o o o o o Thermodynamics of Some~Samarium Cryptate Redox Couples in Various Solvents at 25°C (Ionic Strength 8 001 M) o o o o o o o o o o o Thermodynamics of (Fe0211)3+/2+ Redox Couple in Various Solvents at 25°C (Ionic Strength = 0.1 M) Formation Constants and Free Energies of (EuC222)3+, (EuC222)2+, (EuC2N22)3+, and (Eu02N22)2+ Com- plexes in Water At 25°C (Ionic Strength = 0.1 M). . . . . Formal Potentials and Free Energies + of Transfer of F0 /F0 Redox Couple from Water to Various Solvents at 25°C . . . . . . . . . Free Energies, Enthalpies, and Entropies of Transfer of Europium Cryptate Redox Couples from Water to Various Solvents at 25°C. Page 9” 95 95 97 100 101 Table 19 20 21 22 23 Page Free Energies, Enthalpies, and En- tropies of Transfer of Yb3+/2+, 3+/2+ and (YbC221) Redox Couples from Water to Various Solvents at 25°C 0 O O O O O O O O O O O O O O O O O 102 Formal Potentials and Entropies of Electron Transfer Reactions of Cu2+/+, (CuC211)2+/+ )2+/+’ 2+/+ and (CuCZNlNlN) in Various Solvents at 25°C . . . . . . . . . . . . 106 2+/+ 9 , (CuC2Nll Thermodynamics of (CuC2ll) 2+/+ NlNlN) Redox Couples in Various Solvents (CuCZNll)2+/+, and (CuC2 at 25°C (Ionic Strength = 0.1 M) . . . . 108 Formation Constants and Free Energies of (CuC21l)+, (CuC2ll)2+, (Cu02N11)+, and (0u02N11)2+ Com— plexes in Water at 25°C (Ionic Strength = 0.1 M). . . . . . . . . . . . 109 Free Energies, Enthalpies, and Entropies of Transfer of Cu2+/+, (CuC21l)2+/+, (CuC2 11)2+/+, and N 1 )2+/+ (CuC2 N N Redox Couples N1 from Water to Various Solvents at 25°C (Ionic Strength=0.lM) . . . . . . . 111 xi Table Page 2“ Cavity Radii of Some Cryptand Ligands and Ionic Radii of Some Transition Metal Ions. . . . . . . . . . 11” xii Figure LIST OF FIGURES Page Structural formulas of some typical cryptands. . . . . . . . . . . . . 6 Plots of A03, AH: and TASS of alkali 0222 cryptates (M0222)+ against the size of the correspond- ing cations in water at 25°C . . . . . . . 53 Plots of A03, alkali 0222 cryptates (M0222)+ AH: and TASS of against the size of the correspond- ing cations in dimethylsulfoxide at 25°C. . . . . . . . . . . . . . . . . . 55 Plots of AGE, alkali 0222 cryptates (M0222)+ AH: and TASS of against the size of the correspond‘ ing cations in N,N'-dimethyl- formamide at 25°C. . . . . . . . . . . . . 57 Plots of AGg, AH; and TAB; of alkali 0222 cryptates (M0222)+ against the size of the corres- ponding cations in methanol at 25°C . . . . 3 . . . . . . . . . . . . . . 59 xiii I NTRODUC TIO N The synthesis of a class of macrocyclic ligands known as cryptands by Lehn and co-workers (1,2a),and the demonstra- tion that they can form stable well-defined complexes (cryptates) with a range of ions including the alkali and alkaline-earth metal cations have led to intensive efforts to understand the factors which control the thermodynamic stability of cryptates in solution. The majority of these studies have been conducted in aqueous media; quantitative thermodynamic measurements in other solvents are scarce. One reason is that the magnitude of the stability constants that are expected for many cryptates in nonaqueous media exceed the range that can be reliably evaluated by spectros- copic methods such as NMR (2b). Also, pH titration methods which have proven useful in protic media are obviously in- applicable to aprotic solvents. Cyclic voltammograms of most of the metal ion cryptates including alkali and alka- line-earth cryptates undergoing deposition reactions have shown an irreversible behavior. Therefore no quantita- tive thermodynamic results of these metal ion cryptates can be obtained using cyclic voltammetry. We have found that Tl(I)/T1(Hg) redox couple yields revers- ible cyclic voltammetric behavior in the presence of excess C222 cryptand as well as in the absence of ligand in a number of solvents. Therefore this couple can be used to monitor complexation equilibria for various other metal cryptates, including alkali and alkaline-earth earth cryptates using a competition method. The results are presented and discussed in Chapter (III). We have also been interested in the electron-transfer reactions that involve transition metal ions, since they form the basis of many scientifically and technologically important processes. It is crucial that attempts be made to reach a better understanding of the factors which govern the redox thermodynamics and kinetics of these cations. One effective method to understand the behavior of a metal ion redox couple is to vary its ligand environment in some appropriate fashion. [This variation is often accompanied by changes in the standard potential of the couple, and in the lability of the respective oxidation states, by modi- fication in the degree and type of solvent structure around the metal complex, and by alterations in the mechanism by which electron transfer occurs. Among the numerous ligands which have been or could be employed for such studies are cryptands. Due to their particular structure, these ligands are expected to form substitutionally inert compleXes with both halves of a number of transition metal ion redox couples such as Eu+3/+2, Yb+3/+2, Sm+3/+2, Fe+3/+2 +2/+ in different solvents. and Cu Therefore one can obtain the formal potential of these redox couples. The effect of ligand and solvent on the redox thermodynamics of these couples are described in Chapter V. CHAPTER I HISTORICAL BACKGROUND A. Introduction Interest in cryptand ligands and their complexes with metal cations called cryptates, was initiated when it , was found that these ligands have a tendency to form very stable and selective complexes with different metal ions, including alkali and alkaline-earth cations. Macrobicyclic cryptands containing three polyether strands attached to two bridgehead nitrogens (see Figure 1), were first syn- thesized by Lehn and his co-workers in Strasbourg, France, in 1969 (1,2). Since then, they have synthesized a variety of cryptand ligands such as tricyclic, and tetracyclic cryptands in addition to various macrobicyclic ligands with different active sites and side groups (3-10). In general, the cavity of cryptands are hydrophilic with electro- negative heteroatoms such as O, N, and S binding to the cations, while the outside envelope of these ligands con- taining-CHZ-groups are lipophilic. Macrobicyclic cryptands can adopt three different configurations (ll): (1) exo-exo; where both lone pairs on nitrogens are directed away from the cavity; (2) exo-endo; where one lone pair points into the cavity while the other points away; (A) a = b = 0, c = 1 (B) a = 0 (C) a = b = c = 1 o rm. Swiss/V3 Lo .2 Ow (D) (NJ-cryptand C211 C221 0222 ho")q (UV) 0 O (pa/1) k/°\J (E) [31-cryptand Figure 1. Structural formulas of some typical cryptands. '3‘ (3) endo-endo; where both lone pairs point into the cavity. Weiss and co—workers have determined the crystal struc- tures of a number of the cryptate complexes (12,13). The inclusion complexes have several structural features in common. The metal ion lies within the molecular cavity of the ligand and the cryptand has an endo-endo conformation when it is bound to the metal ion. As mentioned before, macrobicyclic ligands form very stable complexes with alkali metal ions. Indeed, they form the strongest complexes with these cations compared to other ligands such as naturally occurring antibiotics and crown cyclic polyethers. The latter were first synthesized by Pederson (14—16). Investigations of the influences on the stability of the alkali metal cryptates have found that each cryptand has its own size selectivity. For a given cryptand, the most stable alkali metal cryptates has the closest match between the radius of the cation and that of the ligand's molecular cavity. Thus the larger or smaller cations with respect to the ligand cavity would form less stable complexes. The most stable alkali cryptates are L1+C211 (0211 cavity radius=0.8 A (ll), ionic radius of Li+=0.6 A), Na+C22l (0221 cavity radius=l.l A (ll), ionic radius of Na+=l.02 A), and K+0222 (0222 cavity radius=1.u A (11), ionic radius of K+=l.38 A) (17). However, one can— not think of this selectivity as a simple consequence of one cation having a better steric fit into the ligand cavity (18). The observed selectivity is the result of several factors, including the change in enthalpies and the entropies of complexation. In general, the enthalpies of complexation are determined by: (l) the variations in nature and energy of the bonds between the cation and either the ligand or the solvent molecules in the first solvation shell; (2) the change in interaction with the solvent mole- cules outside the first solvation shell; (3) the change in inter-binding site repulsions; (A) the effect of ligand solvation; (5) the steric deformations of the ligand by the cation. The entropy changes on complexation incorporate the solvation entropies of the metal cation and of the ligand, the changes in ligand internal entropy (due to orientation, rigidification, and conformational changes), the changes in total number of particles and in transla- tional entropy. Generally speaking one expects electrostatic com- plexes between hard cations and charged ligands to be entropy stabilized (TAS dominant), whereas the formation of complexes of soft cations containing bonds with more or less covalent character are expected to be controlled by the decrease in enthalpy (AH dominant) (19,20). Thus, the cryptates should belong mainly to the enthalpic type since the ligands are uncharged. However, alkali and alkalin'fearth cations being hard acids, entropy dominant ‘. behavior has also been found. In addition to the extensive studies done on alkali and alkaline-earth cryptates in various solvents, complexa- tion of a number of other metal ions such as heavy and transition metal cations with cryptands have also been studied (17,21-28). Lehn and co-workers (17,21,22) have measured the stability constants of the cryptate complexes formed by C222, C221, C211, and their nitrogen substituents with transition metal and toxic heavy metal cations in addi- tion to alkali, and alkaline-earth cations in water. They have concluded that by substituting nitrogens for oxygens of these macrobicyclic ligands, one can greatly increase the stability of some transition metal and toxic heavy metal ion cryptates, while decreasing the stability of alkali, and alkaline-earth cryptates. Arnaud-Neu gt 2;. (23) have also determined the formation constants of a number of transition and heavy metal ions such as Cu+2, Ni+2, Zn+2, Co+2, Cd+2, Pb+2 , and Ag+ with 0222, 0221, and 0211 in water. Most extensive studies on heavy metal ion cryptates were done on T1+, and Ag+ cryptates (17,23—28). A variety of physicochemical measurements have been used for determination of the stability of cryptates and the determination of enthalpy, entropy or the kinetics of cryptate formation. Detailed description of these tech- niques can be found in several texts (29,30). 10 B. Experimental Techniques 1. Electrochemical Techniques 1.1. Polarography and Cyclic Voltammetry — The great majority of electrochemical studies of cryptates have been carried out by Peter and Cross with propylene carbonate as the solvent (31-39). They found that: (1) the electro— reductions of the cryptates occur at considerably more negative potentials than those for the corresponding sol- vated metal ions; (2) the oxidized form of the alkali metal or alkaline-earth is stabilized by complexation with the cryptand; (3) an electrode of greater reducing power (113;, more negative potentials) is required to reduce such a species to the metallic state; (A) prolonged electrolysis of solutions of K+C222 has shown that the products of the electroreduction of this complex are the amalgam K°(Hg) and the free ligand (38). In a more recent paper, they studied the electro-oxidation of the macrobicyclic ligand (C222) on a gold electrode and in propylene carbonate (A0). The oxidation sites on the ligand were identified and it was demonstrated that the resulting oxidized species no longer complexes the cations. In the cryptates (Mn+0222), the ligand is more difficult to oxidize than the free, uncom- plexed, form. One of the electrochemical studies conducted in aqueous solutions was carried out by Britz and Knittel (41). Their 11 work dealt with an investigation of the adsorption of K+C222 at a drOpping mercury electrode (DME). A combina- tion of droptime measurements and a.c. polarography was employed to determine the maximum surface coverage and the diffusion coefficient of the K+C222 ion. Although alkali metal, alkaline-earth, and transition metal cryptates which undergo deposition reactions, are interesting electrochemical systems to study, due to their electrochemically irreversible behavior, they cannot be used to provide accurate information on the thermodynamics of cryptate formation. However, we have found that the Tl(I)/T1(Hg) couple yields reversible cyclic voltammograms in the presence of excess C222 as well as in the absence of ligand, which has enabled us to obtain thermodynamic complexation parameters for various metal ion cryptates in a number of solvents using a competition method. This method will be discussed in more detail in Chapter III. Cyclic voltammetry has alSo been applied for studying the redox thermodynamics and kinetics of different metal ion cryptate redox couples, where both halves of the metal ion redox couple remains in complexed form and in solution. Gisselbrecht and Gross (42) have studied the electro- chemical reduction cfi‘ mononuclear 00pper cryptates with diaza-polyoxa-po1ythia-ether ligands on platinum electrodes in water and in propylene carbonate. Several points have l2 emerged. S heteroatoms in the macrocyclic ligand stabilize CuI in the cryptate. All the CuII cryptates with thio- ether groups in the ligands are reversibly reduced into CuI cryptates by mono-electronic steps, the standard redox potential of the CuII/I system ranges from -0.10 to +0.A9 V vs SCE in aqueous medium depending on the ligand. Further— more the standard redox potential of the CuII/CuI couple I II) shifts to more positive values (Cu stabilized toward Cu by increasing the number of thioether groups; Weaver gt §l° (A3,“A) studied the thermodynamics and kinetics of complexation of europium and ytterbium in both trivalent and divalent oxidation states with C221 and C222 cryptands in aqueous media using cyclic voltammetry. All _ these cryptates were found to be electrochemically reversible and substitutionally inert on the time scale of cyclic voltammetry. The thermodynamic stabilities of the tri- valent lanthanide cryptates were found to be substantially less than those of the corresponding divalent cryptates, arising from a large enthalpic destabilization outweighing a smaller entropic stabilization. These differences can be understood in terms of the marked dependence of the hydration thermodynamics of the uncomplexed cations upon their charge, and are compatible with the observed complexa- tion thermodynamics for alkaline-earth and alkali metal cryptates having similar ionic radii. The rates of both cryptate formation and dissociation were found to decrease l3 markedly as the cation charge increased from one to three for cations of approximately constant size. These rate differences and also their enthalpic and entropic com- ponents are compatible with the increased changes in cation hydration that are anticipated for cryptate substitution as the cation charge increases. Marked acid catalyses were observed upon the dissociation kinetics of lanthanide cryptates which were ascribed to the need for the cryptate to undergo a conformational change prior to or during release of the cation. The trivalent lanthanide cryptates were also found to associate strongly with fluoride and hydroxide anion to an extent comparable to the aquated cations. 1.2. Potentiometric Measurements - Considering the complexation reaction of the type Mn+ + L 2 ML n+ it is very simple to calculate the formal equilibrium constant for formation of the complex if the concentration of free metal or of the ligand in a solution containing known amounts of the ligand and the metal salt are known. The free metal ion concentration can be determined by potentiometry using ion selective electrodes. These ion-selective electrodes are easy to use and can determine very low concentration of the 14 free metal ion. It should be noted that indicator elec— trodes are cation selective rather than cation specific. Therefore, small amounts of impurities may cause large errors in very dilute solutions. Lehn and Sauvage (17,22) determined the formation constants of some metal ion cryptates using pH electrode as well as cation selective electrodes. Since bicyclic cryptands are diprotic bases their complexing abilities in aqueous solutions depends on the pH of the medium. Therefore titration of the free ligands with an acid in the absence and in the presence of a metal ion yields the values of the complexation constants. A similar technique was used by Anderegg (27) in the study of linear, monocyclic and bicyclic diazapoloxa complexes with several monovalent and divalent cations. Schneider gt a;. (26) determined the stability constants +, and Tl+ by potentia- of cryptate complexes with K+, Ag metric titration in methanol and in several aprotic, polar solvents at various temperatures. The enthalpies and entropies of complexation were calculated from the tempera- ture dependence of the stability constants. Burns and Baes, Jr. (A5) determined the stability constants of some lanthanide tripositive ion complexes with cryptands C222, C221, and 0211 using a potentiometric method. They have concluded that the matching of ligand- cavity size and ion size is not a dominant factor in 15 determining stability in these cryptates. 1.3. Electrical Conductance Measurements - Electrical conductance measurements are relatively easy to carry out in nonaqueous solvents since the vexing problem of obtaining a reversible electrode system in a given solvent is largely eliminated. The disadvantage of the conductance method is its sensitivity to the presence of even small amounts of conducting impurities. The formation of macrocyclic complexes is an ion- molecule reaction and, therefore, complexation results in a decrease in the mobility of the cation due to increase in size rather than in the formation or disappearance of charged-species. Pederson and Frensdorff (16) had already illustrated in a conductometric titration of Na+ with di- cyclohexyl-l8-crown-6 the decrease in conductance as a result of the formation of LNa+. Cox and Schneider (25,A6) determined the rates of dis- sociation of a variety of alkali metal cations and 0a+2 cryptates in several solvents. The reactions were followed conductimetrically by using stopped flow apparatus with conductance detection for faster reactions or a conventional cell. They have also studied the kinetics of the proton transfer reaction between hydroxide ions and the mono- protonated cryptands C211, C221, C222 and C222B in aqueous solutions. Except for C221 the observed relaxation times 16 for the cryptands are consistent with a simple rate- determining proton transfer step (A7). 2. Calorimetric Techniques Calorimetric techniques are extremely useful for the determination of enthalpy of a complexation reaction. Calorimetric methods can also be used for the determination of equilibrium constants, but it becomes unreliable when the formation constants are larger than 10)4 - 105 (29). Pioneer studies on macrocyclic complexation reactions using calorimetric methods were done by Izatt and co- workers (l9,A8,A9). Enthalpies of cryptate formations were studied by Anderegg (27) and particularly by Kauffmann _e_t_a_1_. (18). Abraham £3 £1. (50-52) determined enthalpies of transfer of cryptand 0222 between six solvents, from calorimetric measurements on heats of solution of the cryptand Combina- tion of these measurements with known enthalpies of com- plexation and known enthalpies of transfer of cations enabled the corresponding enthalpies of transfer of the cryptate cations, [M+C222], to be obtained. It was shown that for transfers between two given solvents, values of AH% ([M+C222]) depend on the complexed metal, M+, and hence that single-ion assumptions such as (a) AH° ([M+C222]) = t (C222) and (b) AH° ([M+C222]) = 0 are not generally 0 AH t t valid. l7 3. Spectroscopic Techniques 3.1. Proton Magnetic Resonance (pmr) - Proton magnetic resonance is probably the most used and one of the most useful techniques for the studies of macrocyclic ligands and their complexes in solutions. Many of the unsubstituted crowns and cryptands have very simple pmr spectra which are sensitive to the conformation changes which the ligands. undergo in complex formation. The pmr signal of free C222 consists of a triplet due to N-CMZ, a triplet for N-CHZ-CMZ-O and a singlet for O-Cflz-CM2-O protons (53,5A). Upon complexation, the latter proton resonances are not affected very much by the alkalies but are shifted down-field by alkaline earths. The N-CM2 triplet moves up-field with increasing cationic radius (5A). Formation constant of several complexes were obtained from the analysis of the proton chemical shift dependence on the ligand/cation mole ratio (55). 3.2. ggrbon:l3 Magnetic Resonance - Carbon-13 nmr is a very useful adjunct to the pmr. With present day in- strumentation and, particularly, with the use of Fourier transform spectroscopy, the task of obtaining spectra of unenriched samples is no longer a problem. The range of chemical shifts is much larger than fortfluaproton and the resonance frequencies are quite sensitive to small changes in the conformation and/or the chemical environment 18 of the studied compound. Often 130 measurements are made to confirm the results obtained with pmr (55). Carbon-13 nmr has been used to study intramolecular cation exchange in a [3]—cryptand (see Figure 1(E)) (56). The free ligand shows the expected four 130 resonances. Upon addition of alkali cations the four signals shift smoothly and level off at high M+/E(E=[3]-cryptand) mole ratios. With alkali earth cations, however, the addition of a salt results in the appearance of a new set of four lines. The relative intensities of the two sets change as more salt is added and the signal of the free ligand disappears when 1:1 mole ratio is reached. Further addition of the salt does not change the intensities of the new set of 13C resonances which belong to the complex. Variable temperature study of the 13C resonances of 4.. several metal complexes in D 0 showed that the M oE com- 2 plexes display an interconverting two species in which the cation is located unsymmetrically in the ligand cavity. The protonation of cylindrical macrotricyclic cryptand (see Figure l(D)) and the formation of anionic complexes can be followed very conveniently by 13C nmr (57). 3.3. Nuclear Magnetic Resonance of Nuclei Other Than 1H and 13C - In recent years, with the development of nmr instrumentation, nmr measurements on other non— metallic and metallic nuclei possessing nuclear spins became 19 possible and their use for the studies of macrocyclic com- plexes is becoming increasingly popular. In both.lH and 13C nmr measurements, the studied nuclei belong to the ligand and do not participate directly in the interaction with the metal ion. It is also possible to study the behavior of the ligands by looking at the resonances of the donor atoms themselves, such as oxygen (170) or nitro- gen (luN or 15N). Faster and Roberts (58) studied 15N chemical shifts of cryptand 0211, 0221, and 0222 with alkaline and alkaline earth ions as well as with Ag+ and Tl+. They found that the direction and the magnitude of the chemical shifts varied with the ligand and the metal ion and, in general, depended on charge and ionic character of the metal ion as well as on the tightness of the fit of the ion in the cryptand cavity. Complexation between crown ethers 120A, 1505, 1806, and cryptand C222, and alkali cations Li+, Na+, K+ in various solvents were studied by POpov and Smetana using l7O-nmr, spectroscopy. Small diamagnetic shifts arising from the cation electric field were observed. They in- crease according to the sequence K+ < Na+ < Li+. In general, for crown ethers, considerable line broadening occurs when the cation fits well into the cavity but line narrowing occurs when the cation is much smaller than the cavity (59). 20 Since the macrocyclic ligands are particularly noted for their complexing abilities with the alkali cations, the nmr of the alkali nuclei has been used extensively for the studies of alkali complexes. Magnetic resonance studies of alkali salt solutions in water and in nonaqueous solvents have shown that this tech- nique represents a very sensitive probe of the immediate chemical environment of the respective cations (60,61). The effect of the addition of a cryptand to a lithium salt solution in a given solvent was shown to be very much dependent on the solvating ability of the medium. In the case of the lithium salts, the addition of the larger cryptands C222 and 0221 produces no effect in a strongly solvating solvent such as dimethyl sulfoxide. In less solvating solvents such as nitromethane, the addition of a large cryptand does result in a down-field shift indicating the complex formation but the exchange between the free and complexed lithium ion is fast on the nmr time scale and only one population-average resonance signal is observed (61). On the other hand, with the cryptand 0211, whose cavity size is close to the dimensions of the desolvated Li+ ion, the addition of the ligand to a Li+ salt produces not only a paramagnetic chemical shift but also, in the presence of an excess Li+ ion, two nmr signals are observed corresponding to the resonances of the complex and of the free ion. 21 The kinetics of the decomplexation reaction of Li+- 0211 complex has also been studied in a number of solvents by temperature-dependent line shape analysis (62). The activation energy for the release of the Li+ ion from the complex was found to be related to the donicity of the sol- vent rather than the dielectric constant. The activation energy values vary from 1A.l Kcal mol-1 in formamide to 21.3 Kcal mol"1 in water. Ceraso and Dye (63) found that for the 0222-Na+ com- plexes in ethylenediamine two 23Na signals can be observed at room temperature. Lineshape analysis gave the activation energy of 12.2 i 1.1 Kcal mol-l for the decomplexation re- action. A more detailed study using Fourier transform 23Na nmr gave chemical shifts of free and cryptated sodium ions in several solvents as well as exchange rates and thermo- dynamic parameters of sodium cryptate (6A). Kintzinger and Lehn (65) studied Na+ cryptates with 0222, C221, 0211 and 02282 in 95% methanol solutions by sodium-23 nmr. In all cases when an excess of sodium ion was present, two signals were observed. In the case of. the Na+0222 complex, free energy of activation for the decomplexation reaction at 331°K is 15.A Kcal mol'l which is in agreement with the value obtained from pmr studies (66). The 23Na chemical shifts varied drastically with the ligand. Sodium-23 as well as carbon-l3 nmr were used to study 22 sodium ion complexes with crown ethers 1505, B1505, and 1806 as well as cryptands 0211, 0221, 0222, and 0222B in water and in a number of nonaqueous solvents. The stabilities of the complexes varied in the order Na+-1806 > Na+-1505 > Na+B1505. In most cases the cationic exchange between the free and complexed sites was rapid. However, in the NaBPhu- 1806-THE and NaBPhu-1806-dioxolane systems the exchange was slow enough to observe two 23Na resonances in solutions containing an excess of the sodium salt. Two signals merged when NaBPhu was replaced by NaClOu or NaI. In all solvents studied the four cryptands formed stable complexes with the sodium ion. The limiting chemical shifts showed some solvent dependence in the 30 to -70°C temperature range. The chemical shift of the complexed sodium ion moved down- field in the order Na+0222 < Na+0222B < Na+0221 < Na+0211 (67). Cryptands react with metal solutions in appropriate sol— vents to give the solvated alkali cation and an alkali anion CM+'M‘. Sodium-23 nmr measurements on Na+0222Na‘ salt in methylamine, ethylamine and tetrahydrofuran solu- tions show that for Na' ion the 23Na resonance is shifted strongly up-field from the resonance of Na+ ions (free or complexed) in solutions (68,69). 87 There have not been many studies done on 39K and Rh since the 39K nmr measurements are difficult due to a low 87 sensitivity of the nucleus and Rb resonance yields very 23 broad lines since the nucleus has a very short relaxation time. Preliminary studies of K+-cryptand systems in non- aqueous solvents showed slow exchange between the free and the cryptated K+ ion when 0222 and C221 cryptands were used (70). In a more recent study on potassium complexes with cryptands C222, C221, and 0211 by 39K nmr it was found that the limiting chemical shifts for the K+0222 complex were independent of the solvent, indicating that the cation was located in the interior of the cavity (inclusive complex). The cavities of the other two ligands appear to be too small to accommodate K+ ions, and therefore, the complexes must have an exclusive configuration. In contrast to other two potassium complexes, K+0211 complex showed fast exchange, therefore only one 39K signal was observed. In this case it was possible to calculate the formation constant of the-complex from the variation of the 39K chemical shift with the ligand/K+ mole ratio. The values obtained showed strong dependences on the donor abilities of the solvents and varied between log Kf > A in acetone and no measurable complexation in dimethyl sulfoxide (71). 87 -The only Rb nmr measurements involving cryptate com- plexes are the studies of Dye g3 QM. (69) on the 0222' Rb+-Rb- salt in ethylamine and in tetrahydrofuran solutions. In contrast to 39K and 87Rb, the natural line width of 2A the 133 Cs resonance is very narrow and the sensitivity is relatively high. The addition of the cryptand 0222 to a cesium solution in a nonaqueous solvent produced very strong paramagnetic shifts, in the case of pyridine it goes up to 250 ppm (72). It is seen that in propylene carbonate acetone, acetonitrile and pyridine solutions the plots of 6(ppm) 1s [C222]/[Cs+] show a sharp break at 1:1 mole ratio indicating the forma- tion of a stable complex; while in strongly solvating sol- vents, such as dimethylformamide and dimethyl sulfoxide only very weak complexes are formed. Variation of the 133CS chemical shift for the Cs+0222 complex as a function of temperature was studied in di- methylformamid, propylene carbonate and acetone (73). The results indicate the existence of two types of 1:1 com- plexes. At low temperatures the inclusive complex is pre- dominant, while at higher temperatures only exclusive complex exists. 3.A. Other Spectroscopic Techniques - Other spectros- copic techniques such as electronic and vibrational spectros- copy also have been used. In general, ultraviolet-visible spectroscopy has somewhat limited usefulness for the studies of macrocyclic complexes. Pederson reported changes in the ultraviolet spectrum of benzene-substituted crown ethers upon complexation (15). For example, upon addition of potassium thiocyanate, DB1806 in methanol shows a new 25 absorption band about 6 nm to the larger wavelength side of the major peak. Similar results were obtained by Tusek _p _l. (7A). Shchori e3 g1. (75) determined the stability constants of several DB1806 complexes in aqueous solutions by combining solubility data on the crown with spectro- photometric determination of the total complex concentration. Conformational changes of 0222 in chloroform solutions were studied by Lord and Siamwiza (76) using vibrational spectrOSCOpy. The data indicate that the 0222 molecule is the exo-exo configuration. However, the addition of Ba+2 shifts the spectrum indicating a change to the expected endo-endo structure. ' It has been shown that solvated alkali cations undergo low frequency vibration in the solvent cages. The exact frequencies of such vibrations depend on the cation and on the solvent (77). However, results obtained by Cahen‘ and Popov (78) with cryptands C211 and 0222 showed that the frequency of the vibrational band depends on the metal ion but is independent of the solvents. Gans 22 gl. (79) studied the Raman spectra of sodium and potassium cyanides in liquid ammonia in the presence of 0222. Without the C222 potassium cyanide solution shows two bands in the C-N stretching region corresponding to the free solvated anion and anion in the K+CN' ion pair at 2056 and 205A cm-1 respectively. In the presence of 0222 the band for the ion pair is no longer visible, since 0222 re- acts quantitatively with the potassium ion. CHAPTER II EXPERIMENTAL 26 A. Apparatus Electrochemical measurements were done using conven- tional glass cells with working and reference compartments separated by "very fine" or "ultra fine" grade frit ob- tained from Corning, Inc. The working compartment had a volume capacity of 5-10 ml. The frits used had an average porosity of 1-3 um, hence preventing significant mixing of two solutions in reference and working compartments on the time scale of 2-3 hours required for most experiments. To control the temperature of the solution in working compart- ment within i0.05°0, the working compartment and part of the salt bridge between working and reference compartments were surrounded by a Jacket through which water from a Braun Melsungen circulating thermostat could be circulated. In all measurements the working and reference compartments were filled with the same solution, hence solvent Junction was formed between the aqueous reference electrode and the nonaqueous solution in the reference compartment. Cells used for bulk electrolysis had a separate com- partment for counter electrode which was separated from the working compartment by means of a frit. 27 28 B. Electrochemical Techniques 1. Common Features All nonaqueous solutions were prepared in dry box under nitrogen atmosphere. The solutions were deoxygenated by bubbling with prepurified nitrogen which had been passed through a series of wash bottles containing concentrated H280“ and finally through the bottle containing the non- aqueous solvent of interest. For aqueous solutions, pre- purified nitrogen was passed through V(II) and finally water. Nitrogen gas was always saturated with the solvent of interest in order to prevent extensive evaporation of the solvent during the experiment. In all experiments, a saturated aqueous calomel elec- trode (SCE) filled with saturated NaCl solution was used as the reference electrode, and a platinum wire served as the counter electrode. 2. Cyclic Voltammetry A PAR 17AA polarographic analyzer (Princeton Applied Research Corp.) coupled with a Hewlett-Packard HP 70A5A X-Y recorder was used to obtain cyclic voltammograms. Sweep rates used in this work were in the range of 50-500 mV/ sec. Peak potentials could be measured with a precision of i1-2 mV using the above instrumentation. Working electrodes used in the cyclic voltammetric 29 studies were: hanging mercury drop electrode or HMDE (Metrohm Model EAlO, Brinkmann INstruments), glassy carbon, and platinum "flag" electrode. Due to anodic limitation of mercury HMDE can only be used for redox couples with relatively negative standard potentials, so for work at positive potentials, a glassy carbon or platinum flag electrode was employed. The latter consisted of a 2 mm2 sheet of platinum foil spot-welded to a fine platinum wire. The platinum flag electrode was pretreated by immersion in warm 1:1 HNO3 followed by activation by passage over a Bunsen burner flame. 3. Preparative Electrolyses 2 For preparing Eu+ , Yb+2 2, constant-potential , and Sm+ electrolyses were performed with a PAR 17AA potentiostat. A stirred mercury pool and a platinum gauze were used as working and counter electrodes, respectively. During each experiment, the electrolyzed solution was kept under de- oxigenated nitrogen atmosphere to prevent any reactions with atmospheric oxygen. A. pH Measurements A Corning Digital 109 pH meter combined with a regular glass electrode was used for pH measurements. 3O 0. Materials l. Cryptates 2 2 2 2 2 The Eu0222+ , Eu0221+ , Yb0222+ , Yb0221+ , Sm0222+ , and Sm0221+2 complexes were made by electrolyzing solutions of Eu+3, Yb+3, and Sm+3 at the appropriate potentials to their divalent states, then slight excess of the appropriate cryptand was added to the solution. Solid lanthanide cryptate samples were obtained from Dr. 0. A. Gansow's group. The Eu0221.013, Eu0222.013, Eu0221.- (N03)3, EuC222.(NO3)3, and YbC22l.Cl3 complexes were syn- thesized by mixing the appropriate Eu or Yb salts with the cryptand in acetonitrile. After refluxing this solution for a few hours, the complex is precipitated from solution by the addition of diethyl ether (80). By mixing Sm(ClOu)3 with 0222 or 0221 in acetonitrile at AO°C Sm0222+3 or Sm0221+3 was formed instantaneously in the solution. 2. Reagents Mercury used in the HMDE and as the pool electrode in electrolyses was triply distilled under vacuum (Bethlehem Apparatus Co.). Cryptands 0222, C221, and 0211 were obtained from PCR, Inc., and used without further purification. Other cryp- l l were kindly sup- tands such as C2N22, C2Nll, and 02 N N N plied by Dr. Lehn. 31 All the salts used in this work were analytical grade and used without further purification, except for tetra- ethylammonium perchlorate (Eastman), which was recrystal- lized from water and dried in a vacuum oven at 80°C. Eu(ClOu)3.6H20 (Alfa), Yb(ClOu)3.6H20-(Alfa), and Sm(010u)3.nH20 (ROC/RIC) were dried at 100°C in a vacuum oven. Dehydrated perchlorate salts of potassium (J. T. Baker Chem. Co.), and magnesium (MCB), were dried under vacuum at 150°C and 60°C respectively. Ca(010u)2.6H20 (G. F. Smith) was dried at 1A0°C for 2A h under vacuum. Dehydrated perchlorate salts of Na, Li, and Cs (all obtained from G. F. Smith Chemical Co.) were dried for several days at 110°C, 190°C, and 180°C, respectively. Cu(ClOu)2 and Fe(0104)3 (G. F. Smith) were dried at AO°C in a vacuum oven for several days. T1010“ was synthesized by mixing stoichiometric quanti- ties of T12003 (Alfa) and H010”. The solid brown impurity was then removed by filtration, and the filtrate was con- centrated to about a quarter of its original volume. The solution was cooled and T1010“ was allowed to crystallize from the solution. Ferricinium picrate (F0+) was prepared as described in Reference (81). 3. Solvents Water was purified by the use of a Milli-Q purification 32 system (Millipore Corp.). Propylene Carbonate (Aldrich) and N,N-dimethylformamide (Aldrich, "Gold Label" grade) were refluxed overnight under reduced pressure over CaH2 and P205, respectively, then fractionally distilled and only the middle 70% fraction was collected. Dimethyl- sulfoxide, methanol, and acetonitrile were Aldrich "Gold Label" grade. Formamide and N-methylformamide were pur- chased from Eastman and Aldrich, respectively. Most of the mentioned solvents were kept over freshly activated molecu- lar sieves (Lind Type 3A), and the water contents were determined to be <0.05% by an automatic Karl Fisher. All the solvents were kept in a dry box under a nitrogen atmos- phere. CHAPTER III THE THALLIUM(I)/THALLIUM AMALGAM COUPLE AS AN ELECTROCHEMICAL PROBE OF CRYPTATE THERMODYNAMICS IN NONAQUEOUS SOLVENTS 33 A. Introduction Although alkali and alkaline-earth cations play an important role both in chemistry and in biology, their co- ordination chemistry has mainly been developing in recent years with the advent of synthetic macrocyclic and macro- bicyclic ligands. These ligands form inclusion complexes in which the metal cation is contained in the intramolecular cavity. In order to reach a deeper understanding of the thermo- dynamics of cryptate formation, we have determined the entropy ASS and enthalpy AH: of cryptate complexation in various solvents. I Thallium 0222 cryptate redox couple was used to determine the thermodynamics of formation for alkali and alkaline- earth 0222 cryptates in various solvents using a competition method (82). B. Results While the amalgam-forming electroreductions of the Cd+2 and Pb+2 cryptates were irreversible, the correspond- ing reaction for T1+C222 was found to be electrochemically reversible in a number of solvents such as water, dimethyl- sulfoxide (DMSO), N,N-dimethylformamide (DMF), and methanol. 3A 35 Thus cyclic voltammograms of solutions containing T1+ and at least a ten-fold excess of 0222 had sweep-rate— independent peak separations of about 60 mV, which is quite close to the value expected for a reversible one-electron process (111). Reversible Voltammetric behavior was also obtained for the Tl(I)/T1(Hg) couple in the absence of the ligand in the solvents listed above. The voltammetric half— wave potential E1/2 was obtained from the mean of the cath- odic and anodic peak potentials. The dependence of the voltammetric "half-wave" potential El/2 upon the excess cryptand concentration [C] was observed to be in accordance with the simple Lingane equation for the reversible amalgam-forming reduction of labile complexes of high stabil— ity (83): TIC T1 T1 El/2 - E1/2 = -(RT/F)[2nKS + m AnEClE] (1) T1 T10 where El/2 and E1/2 are the half-wave potentials for the Tl(I)/T1(Hg) couple in non-complexing media, and in the presence of a large excess of cryptand, respectively, K31 is the stability constant of the thallium(I) cryptate TlCm, and [C]t is the total (analytical) concentration of cryptand. The analysis of this dependence using Equation (1) yielded m = 1 in all solvents; ;;e;, Tl+ forms a 1:1 complex with 0222, as expected. The values of stability constants 36 obtained for T1+C222 complex in a number of solvents agrees quite well with the values reported in the literature, as shown in Tables l-A. The reversible electroreduction of the T1+0222/T1(Hg) couple indicates that the exchange between Tl+ and Tl+0222 is rapid on the time scale of cyclic voltammetry (2-3 sec-l). This finding is consistent with the rapid exchange rates ob- “ sec.l (11)L Irreversible tained from nmr measurements (10 cyclic voltammograms were observed for the electroreduc- tion of T1+C222 in propylene carbonate (2A). However, only a stoichiometric amount of cryptand was present in the experiments described in Reference 3A. These conditions render the interpretation of the results difficult since the conventional treatment of labile complex-forming systems requires the ligand to be present in a large excess relative to the electroactive metal ion. In the present investi- gation, the concentration of 0222 was always at least ten times that of Tl+. A From the form of Equation (1), it is seen that the T1+, Tl+0222/T1(Hg) system provides a direct means of monitoring the activity of free cryptand. Such systems can be classified as electrodes of the second kind and have been labeled "metal complex" electrodes (85,86). Such couples provide a route to the determination of stability constants for other electroinactive cations using a com- petitive complexation method (85 86). A method of this 37 type can be employed to determine a wide range of stability constants by using the following procedure. The half— wave potential, E1/2’ for the Tl(I)/T1(Hg) couple was Tl ) 1/2 ’ and then after successive additions of m5—1O mM 0222 (E determined in solutions containing m0.5 mM Tl+ (E TIC) 1/2 ’ and m15—50 mM of the electroinactive metal cation M (Efigc). The ionic strength was maintained at the desired value using tetraethylammonium perchlorate (TEAP). Reversible cyclic voltammograms were obtained in all'cases, except when Rb+ was added to the methanol and water solutions and Ca+2 to the methanol solution. In general it was observed that Tl TlMC T10 TlMC Tl ”El/2 < -E1/2 < -El/2’ the proximity of El/2 to El/2 or E$}g depending on whether or not M could compete effec- tively with Tl+ for the cryptand. In order to determine the required stability constant K2, it is necessary to know the equilibrium concentrations of the metal cryptate [M0], the metal ion [M], and the free cryptand in the presence of M, [C]M. As outlined below, [C]M can be determined from the electrochemical data. Knowing [C] the remaining M’ terms [MC] and [M] can be found directly since [M0] 2 [Clt - [C]IVI and [M] = [M]t - [MC], where [M]t is the an- alytical concentration of M. (Strictly speaking, [M0] = [C]t - [C]M - [T10], but the last term is usually quite small relative to the others and its neglect represents an error of 3-5%. If necessary, [T10] can be calculated from T1 [C]M, KS , and the analytical concentration of Tl+, [T1+]t.) 38 The determination of [C]M can be accomplished by noting that Buck's equation for the effect of complexa- tion upon reversible voltammetric waves (87) can be written for the competition experiment as T1 . K [C]M+1 TlMC Tl _ RT T1 RT s E1/2 E31/2 "" Tlnms Emu) " Fm T1 (2) Ks [01M (the activity coefficient terms are omitted from Equations (1) and (2) and elsewhere for simplicity.) Although Buck's equation normally only applies to the case where the free ligand is in large excess (88), it should apply in the present case even though the free ligand concentration [C]M is typically less than the total thallium concentration [Tl]t. This is because the cryptand concentration will be "buffered" provided that [C]t >> [let and equilibrium M + 0 I M0 is maintained during the cyclic voltammogram. (If this is not the case, then the shape of the voltammo- gram will be severely distorted since the concentration of cryptand increases during the cathodic part of the :1 from Equation (1) T1 in the absence of metal ion M and then inserting Ks into cycle.) Consequently, by obtaining K Equation (2), one can determine [C]M and hence Kg. In particular it is interesting to note that when K:1[C]M >> 1 (112;: when the stability of the thallium cryptate is sufficiently greater than that for the competing metal cryptate so that EE}2 - Eiigc g 100 mV), the last term in 39 Equation (2) can be neglected, which allows Equation (1) to be subtracted from Equation (2) to yield TlMC TIC E1/2 .- 131/2 = !g: unto]t - inthM) (3) In this case, [C]M and K2 can be determined directly from Equation (3). This procedure does not require a knowledge of Kgl. Therefore, under these conditions, the Tl(I)/ Tl(Hg) couple responds only to the decrease in free cryptand concentration which results when an excess of metal ion Tl M is added. It is noteworthy that KS is not needed for a determination of K2 under these circumstances. In non- aqueous solvents, it is possible that the small concentra- tion of T1+ (0.5 mM) is preferentially complexed by water and other impurities, which could lead to false values of Kgl. These incorrect Tl stability constants will not effect the K? measurements unless the impurities vary in concentration upon the addition of M, or if they are cap- able of binding significantly to the much higher (10-50 mM) concentrations of M that were present in these experi- ments. It is also important to note that [C]M can be calculated using Equation (2) or (3) even when [C]M << [C]t, and that the method is generally capable of allowing K? to be obtained even when K2 << K21. In fact, the M s that can be determined using practical lower limit of K A0 this method is simply that which corresponds to appreciable cryptate formation at the concentrations of M and C chosen. :1 lies in the range 106 - 1010 in the solvents studied, the method described here allows 10 Since we find that K values of K? in the range ca. 10 to 10 to be accurately M 5 evaluated. (It is difficult to obtain K values when K: > Kgl since the Tl+ ceases to be an effective competitor. In practice, the difference between ET1 and ETlMC becomes 1/2 l/2 too small to be measured reliably.) Tables l-A list the values for stability constants AH° as well as AG° c’ 0’ and A83 for complexes of thallium, alkali metals, and some alkaline earth-metal cations with cryptand 0222 in H20, DMSO, DMF, and MeOH, respectively. It is seen that good agreement is obtained between the present and earlier determinations of these thermodynamic values (17,18,25—27,52,89). It is important to note that the values of enthalpy of cryptate complexation AH: ob- tained indirectly from the known values of free energy AG: and entrOpy AS; (this work)are in very good agreement with the values obtained directly from calorimetric measure- ments (18,27,52). The free energies of complexation can be determined from values of stability constants using the following equation 0 _ AGc - -A.57 T log KS (A) Entropies of complexation were determined from the slopes Al NH o.mv mo.o xgos page o.Hv mo.o ms.o m+mz em a.:. me: m.mHu m.mu m.a H.o NH m.© mo.o xpoz . page 0.:. ma: e.meu s.m- a.e mo.o om.e +He NH o.mv no.0 xpoz page o.Hv mo.o os.H +ao em m.mu Hm- m.HHI m.mn H.: H.o ma a.m- on- a.efl- a.m- m.s no.0 as.a +aa em a.mu m.HHu o.HHu m.su m.m H.o we m.au an: a.HHu m. m.m mo.o xpoz page s.mu m.meu H.Heu a.s- :.m mo.o mm.H +x em m.Hu on 3.»: m.mn H.= H.o NH H.NI NI =.NI m.ml m.m mo.o xpoz ance m.Hu a- a.su o.mu H.a mo.o mo.H +az AH o.mv mo.o xgoz were o.Hv mo.o mm.o +Hn a. opHQm AHOE\HNOKV Ax. HOP—\HNUV A.HOE\HNOVAV AHOE\HNOV~V WM woq wflzv Afiv COHUNO wmae wmo wma woo _ smemmmwm apnoea .OOmm pa tops: on conooesoa mmmo+cz do noesnsaooesore .H canoe A2 m.onwc< ”H.0nmx woa "ohm xpoz wasp Lou .a.o mnwma . Hoe Hoax m.o .Hl mofiucfimppoocs Hmucosfipmdxm* a Nm 0.0 cm m.ou m.m| 0.: H.o ma m.m m.mH m.on o.mu 3.: mo.o xgoz mane m.m Hm m.on m.mt m.z no.0 oo.H m+mo annex Aaofi\amoxv x.Ho%\HmoV Aaoemamoxv Aaosmamoxv mm woq sz Amv coapmo om<9 om<. om< ou< camcogum manomm ca20H .oossancoo .H canoe “3 O O taos Hoax m.owoo< ”H.owmm woe .s.o mnwma .Hl HOE Hmox m.o ,homq «H “ohm xpoz was» now mofiucfimupooc: Hmucoefigodxm * xpoz - wane o.m oa+ m.Ht 0.3: m.m mo.o oo.H m+mo xpoz maze o.Hv mo.o mN.o m+wz mm m.ml m.m H.o xgos mfine m.m| HHI :.HHI o.ml o.m mo.o om.H +HB mm :.H No.0 xpoz mane H.ml NH: o.NI w.Ha :.H mo.o 0N.H +mo xgos mane m.wl mm: m.:HI m.Nt m.m mo.o m:.H +nm mm H.mt NH: m.:HI 3.0: m.o H.o xpoz mane m.m| Hm: m.mal :.m| m.w mo.o mm.a +x xpoz mane w.Ht m.mt ©.ml o.NI m.m mo.o mo.H +mz xhos mace o.Hv mo.o mm.o +HA m atmom AHoE\Hmoxv Ax.HoE\HMoV AHoE\Hmoxv AHOE\HmoxV x woq mwzv A v coapmo o o 0 con m: m \l/ .m manna .OOmm on oofixoeHanasooeAm ca doesnEEom mmmo+cz no aofisacsoossone AA A Hos Hoax m.onwo< ”H.0aax mod .s.o mnwma ”Hueoe Hoax m.o nom< at "one xpoz was» you mofipcfimugoocz anacosfipodxmm VTHO3 .51.. mass m.:+ sa+ m.mn H.wu m.m mo.o oo.H mo xgoz . . . m+ mass 0 av mo 0 ms 0 +mmz mm m.mn ma- m.mfiu m.oa: e.s H.o xgoz were H.mu NH: m.man 5.0Hn m.s mo.o om.a +He mm m.zn ma: m.s- m.mu m.m No.0 mm m.mu ma- o.su H.mn m.m Ho.o xgoz were m.:: can H.mu H.mu :.m mo.o os.e +mo xpos nfine m.mn Hm: m.mHn m.ma s.o mo.o m:.a +om om m.Hn m.o n s.mHu m.oau m.s H.o xpoz mane m.:u we: m.meu s.oHu m.s mo.o mm.H +x xhoz mass m.:: :H. a.mHu m.mu H.© H.o mo.e +cz xhoz page m.Hv mo.o mm.o +fiq .eom AHoE\Hmoxv Ax.HoE\Hcov Aeos\eooxv AHoE\Hsoxv we won sz Axv coepmo * wmae wma who won zcmcotpm nsfionm cacoH .Oomm um OUHEmELOMHNSUGEHQI.Z.Z CH coaumegom mmmo+cz mo mOHEMCNUOELoSB .m canoe A5 00 00.0 00.0 00.0 +00 mm o.NHI 00 0.00- 00 0.00- 0.00 00.0 00 0.0a 00.0 x003 0000 0.0- 00: 0.00: 0.00: 0.00 00.0 x003 0000 0.0: 00: 0.00- 0.00: 0.00 00.0 00.0 +0 mm v.00: 00 0.00: 0 00 0.00- 00.0 00.0 00 0A 00.0 x003 00:9 0 0 0.00: 0.00: 0.0 000.0 00.0 +02 00 0.0 00.0 xLoz 0000 0.0 00 0.0 0.0: 0.0 00.0 30oz 0.0.02.0. ©.m m0 m.0+ mlmt N.H mo.o x003 0000 0.0 0.00 0.0+ 0.0- 00.0 0.0 00.0 +00 hhmm AHOE\H.®OXV AK.HOE\HGOV AHOE\HQOV~V AHOE\HGOV~V MK wOwH AEV A v COfiUwU o o mach m: m wm 0; (b) AH < O and dominant, TAS < 0; (c) TAS > O and dominant, AH < 0; (d) TAS > 0 and dominant, AH > 0. Cases (a) and (b) are enthalpy stabilized complexes and (c) and (d) are entropy stabilized complexes. The complexation features depend on the enthal- pies and entropies of cation solvation which are higher for smaller and more highly charged cations. Thus all four types of complexes (a) - (d) are found among the cryptates studied here depending on the cation and solvent. The enthalpic stabilities of the Na+C222, K+C222, Rb+C222, CS+C222 and Tl+C222 cryptates are in general sev- eral kilocalories higher than their free energy stabilities because of negative entropy changes (type b). The Ca+2- C222 complexes in the solvents studied are of type (c). The stabilities of the Ca+2 C222 cryptates in different solvents are entirely of entropic origin but none is ap- preciabl* endothermic (AH > 0). Positive entropies of ”9 complexation are found for the small cations such as Li... and Mg+2. These cations have large solvation entropies so that release of the solvation shell on complexation gives a relatively large positive entropy change, which compen- sates the positive enthalpy, and results in a stable complex (case d). As mentioned in Chapter I the enthalpies of complexation contain: (1) the variations in nature and energy of the bonds between the cation and either the ligand or the sol— vent molecules in the first solvation shell; (2) the change in interaction with the solvent molecules outside the complex as compared to those outside the first solvation shell (Born term); (3) the change in inter-binding site repul— sions; (H) the effect of ligand solvation; (5) the steric deformations of the ligand by the cation. Since dimethyl ether has a smaller dipole moment (1.30D) than the four solvents used in this study (dipole moments of H20, DMSO, DMF, and MeOH are 1.85, 3.90, 3.86 and 1.7, respectively) and the ligand shell is thicker (11) than the first solvation shell, both terms (1) and (2)- should destabilize the complexes with respect to the sol- vated state. Therefore the measured favorable enthalpies arise in a large part from factors (3) and (u). Factor (H) plays an important role in the stability of macro- cyclic complexes (91) since the macrocyclic structures are less solvated than the non-cyclic ligands and thus 50 complexation requires less solvation bond breaking. Effect (3) is also important. Repulsions between the solvent molecules forming the solvation shell destabilize the solvated state and this destabilization increases more and more for each new solvent molecule brought into the shell, whereas the linkage of all binding sites in a suitable arrangement in a single polydentate ligand first supresses this destabilization effect and second, allows the introduc- tion of more binding sites than the balance between cation- site attraction and site-site repulsion permits in the sol— vated state. Effect (5) plays a role for those cations which are too small or too large for the intramolecular cavity (C222 cavity radius=l.ufi). The positive enthalpies of complexation observed for Li+C222 and Mg+2C222 probably arise from the small size of the cation (see Table l for cationic radii of these ions). The entropies of complexation are much less positive than one might expect on complete release of the solvation shell; in fact even marked entropy losses are observed in most cases. An appreciable negative entropy change upon complexation is expected to arise from a rearrangement of solvent structure on cryptate formation. Complexation of a metal cation by a cryptand transforms a small inorganic cation into a large hydrophobic organic cation. This should lead to a marked loss of entropy due to solvation of "the second kind", i.e., the formation of a solvent 51 structure around the organic cation (92). Lehn and co- workers (18) chose NBuZ as a model for a hydrOphobic cryptate cation, and determined the entropy changes for the + + process M + NBuu in water. They obtained entropy losses + of about ~10, -17, -2u, -27 and -28 e.u. for M = Li+, Na+, K+, Rb+, and Cs+, respectively. Other factors responsible for negative entropies for cryptate formation are the changes in ligand internal en- tropy such as conformational changes and changes in transla- tional entropy. The entropy loss due to the latter factor is about -10 e.u. 2. Enthalpy and Entropy Contributions to Cryptate -Selectivities As shown in Figures 2-5 the enthalpies of complexation of the cryptates present selectivity peaks and show almost the same trends as their free energies. By contrast, the en- tropies of complexation generally show the same sequence and become less positive or more negative as the cation becomes larger or has lower charge. This is in agreement with the larger entropy gain one expects upon complexation of small and highly charged cations which display large entropies of solvation. Therefore, the selectivity peaks observed in the stability constants of the cryptates are entirely of enthal- pic origin. Lehn and coworkers (18) have concluded that for cations + of the same charge, the selectivity M (larger)/M+ (smaller) 52 Figure 2. Plots of AG: (solid line), AH: (dashed line) and TASS (dotted line) of alkali C222 cryptates (M0222)+ against/the size of the corresponding cations in water at 25°C. k col/mo! .1. O I 01 53 N 0’ K‘ Rb’ Cation -Figure 2. 5“ Figure 3. Plots of AG; (solid line), AH: (daShed line) and TASS (dotted line) of alkali C222 cryptates (MC222)+ against the size of the correspond- ing cations in dimethylsulfoxide at 25°C. 55 -45‘ D . _oE\_oo x Cs” K“ Rb’ Cofion No’ Figure 3 56 Figure 4. Plots of AG: (solid line), AHg (dashed line) and TASS (dotted line) of alkali C222 cryptates (MC222)+ against the size of the corresponding cations in N,N'-dimethylformamide at 25°C. k col / mol -I7 57 l No’ K1+ Rb 05* Cation Figure h 58 Figure 5. Plots of AG: (solid line), AHg (dashed line) and TASS (dotted line) of alkali C222 cryptates (MC222)+ against the size of the correspond- ing cations in methanol at 25°C. k col /mol 59 60 is higher in terms of enthalpy than in terms of free energy. Whereas C211 and C221 have a high free energy selectivity for L1+ and Na+ respectively, the Na+C2ll and Na+C221 cryptates display about the same AHC. The preference of 0221 for Na+ over K+ (AAGC a -l.8 Kcal/mole) is reversed in terms of enthalpy (AAHc = -1.N Kcal/mole). Thus the cavity radius/cation radius effect used as an empirical criterion for discussing the selectivity of com- plexation (l7) incorporates both enthalpic and entropic effects and is not Just a measure of steric fit. The M+2/M+ selectivity is completely different in terms of free energy as compared to enthalpy alone. Although di- valent cryptates are usually more stable than monovalent ones (with cations of similar radii), their enthalpy of complexation is smaller, so that the enthalpic M2+/M+ selectivities may be reversed. 3. Solvent Effects on the Thermodynamics of Complexa- tion From the results in tables l-M, it is clear that the transfer from aqueous solution to DMSO, DMF, or MeOH solu- tion increases the stabilities of the cryptates by factors of the order of 102 - 105. This marked increase in the stability of cryptates in non—aqueous solvents is due to a marked increase in enthalpy of complexation, the complexa- tion entropies becoming even more negative than in water 61 (exceptions are Na+C222 and K+C222 in MeOH). The much higher enthalpies of complexation in non-aqueous solvents which result in higher stability constants may be due in a large part to the increased electrostatic interaction of the cation with the ligand in the medium of lower dielectric constant and its smaller interaction with the solvent. Another factor responsible for higher stability constants in non-aqueous solvents is that the free cryptands in- cluding C222 are considerably more strongly solvated in aqueous solution (26). More information on the ability of cryptand C222 to isolate the metal ions from solvent molecules can be ob- tained from the values of the absolute entropies of the metal ions S° in a given solvent (90) and entropies of complexation of the corresponding cryptates A82. The en— tropy of complexation AS: is given by the following equa- tion: .. _ _ + ' A33 = S°(MC222)+ - (S°(C222) — S°(M ) (6) where S°(MC222)+, S°(C222) and S°(M+) are the absolute entropies of the metal ion C222 cryptate, the cryptand C222 and the metal ion, respectively. Equation (6) can be rearranged as as: + §°(M+) = sow-c222)+ - s° (7) 62 By subtracting Equation (7) for two metal ions in a given solvent from one another the unknown value of S°(C222) will be cancelled: [ASZ(KC222+) + S°(K+)] - [Asg(M0222+) + §°(M+)]‘= - + o + S°(KC222) - S (MC222) (8) It is clear that the values of [S°(KC222)+ — S°(MC222)+] can provide some information about how well the cryptand C222 can isolate the metal ion from the surrounding solvent. These values, as well as values of [S°(K+) - S°(M+)] in different solvents, are given in Table (5). It should be noted that K+ has been chosen as the reference, since it best fits the cavity of cryptand 0222 with respect to other metal ions studied here. The results in Table (5) show that the absolute values of [82(K0222)+ - §°(MC222)+] are in general less than that of [S°(K+) - S°(M+)], and are not equal to zero. These results indicate that the cryptand C222 is only capable of partially isolating the metal ion from the solvent mole- cules. The degree of isolation depends entirely on how well the metal ion fits inside the cavity of cryptand. Metal ions which are either too large or too small for the cavity of cryptand C222, such as Cs+ and Li+, have large abSIlute values of [§°(Kc222)+ - S°(MC222)+], while these 63 Table 5. Absolute Entropy Differences of K+ and Various Alkali Metal Cations, and the Corresponding Differences of K+0222 and Various Alkali Metal C222 Cryptates in a Number of Solvents. [§°(K+)-S°(M+)] [§°(Kc222)+-§°(Mc222)+] Solvent Cation (cal mol'lK’l) (cal mol'l K—l) MeOH Li+ +15 -7.5 H20 Na+ ' 10.1 3.6 DMSO Na+ lu.3 -l.2 DMF Na+ A.3 2.3 MeOH Na+ 7.8 -2.2‘ H20 m)" -5.2 2.3 DMF 05+ -6 -6 MeOH . Cs+ -7.9 11.1 6A values for Rb+ and Na+ are small and close to zero. + It is interesting to note that the value of [S°(KC222)MeOH - S°(CsC222);eOH] is large and positive, while it is ex- pected to be negative. This might be due to the fact that Cs+ forms an exclusive complex with cryptand C222, where part of the cation is in direct contact with solvent molecules. Therefore, S°(CsC222)+ becomes more negative than §°(x0222)+. CHAPTER IV TREATMENT OF ELECTROCHEMICAL THERMODYNAMIC DATA FOR COMPLEXING REDOX COUPLES 65 A. Determination of Complexation and Transfer Free Energies The formal Galvani potential 0f of a redox couple in a given solvent (i.e., the formal Galvani potential dif- ference between the electrode phase and the bulk solution) is sensitive to the chemical nature of the coordinated ligands, the metal center, the charge on the reactant and the nature of the solvent. Therefore, variation in the co- ordinated ligands (first coordination shell), or the sol- vent, results in changes in the formal Galvani potential. These changes in 0f can provide valuable information about the separate effects of the ligand (142;, the primary co- ordination sphere), and the solvent (the secondary solva- tion sphere and beyond) on redox thermodynamics of the metal ion redox couple. Considering the following equilibria: MIII(solvent) + e- (T, electrode)_r___l:}MII (solvent) (1) III ‘ G0 0 K (A III,L) KII(AGII,L) O ‘ III — Aer d'll MLx (solvent) + e (T, electrode)0r———_ LX (solvent) (2) 66 67 One can relate the difference in Galvani potentials of the uncomplexed and complexed metal one electron redox couples (¢f(MIII/II) - ¢f(ML;II/II)) directly to the difference in the free energy driving force for these processes (AA): III/II III/II _ ¢f(M )-f(MLx ) - (2.303RT/F) log(KIII,L/KII,L) = (AGTI,L ‘ AGTII,L)/F = A(AG°)L-S/F (3) where AGTII,L and AGTI,L are the free energies of complexa- tion for the trivalent and divalent species, respectively, and K and KII L are the corresponding stability ’ III,L constants. Since single values of or cannot be determined ex- perimentally (generally electrical potential differences_ can only be measured between two phases of identical chemi- cal composition, such as a pair of metal electrode ter- minals), the experimental configuration is to combine a working electrode with a reference electrode, having a stable equilibrium value of ¢ref (93). Therefore we can write: ¢f = Ef - ¢ref - $23 (A) where Ef is the formal cell potential, which can be 68 measured experimentally, 0 is the Galvani potential dif- ref ference formed at the reference electrode, and 013 is the liquid Junction potential formed between the solutions in the reference and working compartments. Since in a given solvent oszand ¢ref remain constant, Equation (3) can be written as: ¢f(MIII/II)-¢f(ML§II/II) = Ef(MIII/II) - Ef(ML§II/II) = (2.3O3RT/F)1og(KIII,L/KII’L) = (AGTI,L ‘ AGTII,L)/F = A(AG°)L'S/F (5) One can write a similar equation to Equation (3) for free energies of transfer of a redox couple from water to a nonaqueous solvent: 0 (MLIII/II, solvent A) - t (MLIII/II, water) = f' x f X (2°3O3RT/F)l°g(KIII,s-w/KII,s-w) _ o _ o ‘ (AGII,s-w AGIII,s-w)/F = a(AG;C)S'W/F (6) 69 Since the changes in the formal Galvani metal-solution po- tential difference A(f)s-W corresponding to the measured changes in formal potential, AEg'w, for a given redox couple between pairs of solvents "s" and water, equation (6) can be written as: A(AGrc) F(AEf A¢£j ) (7) where, Adigw is the change in the liquid junction potential between the working and reference compartments brought about by substituting solvent "3" for water. Therefore, the estimation of the free energy of transfer of a redox couple from water to a non-aqueous solvent [A(AG;C)S'WJ requires an extrathermodynamic assumption. There are various methods available by which such transfer free energies can be esti- mated to a reasonable approximation of about 1-2 kcal/mole (9A-101). The simplest method for electrochemical purposes in- volves the ferrocene assumption. This model was originally introduced by Strehlow and his coworkers (95), and involves the assumption that the formal Galvani potential of of the ferricinium-ferrocene (Fc+-Fc) redox couple is independent of the solvent. This means that the difference in the solvation energy between ferricinium and ferrocene is solvent independent; liiia AGt(Fc+) = AGt(Fc). As men- tioned before, this method is particularly convenient for 70 electrochemical determinations of the free energy of single ion transfer, AGE, since AG; can be estimated simply from the solvent effect upon the measured standard electrode potential for the apprOpriate cell reaction relative to the corresponding potentials for Fc+/Fc under the same condi-. tions. However, the use of the ferrocene assumption has been shown to yield significantly different estimates of AG; thermodynamic approaches, particularly when one of the sol- compared with those obtained by using other extra- vents is water (9A,96-99). There are several reasons for the inadequacy of Fc+/Fc for estimating the thermodynamics of transfer of single ions. Among them are: the small radius of the ferricinum (Fc+) ion, which can give rise to ion-dipole interaction and cause solvent dipoles to orient toward the ion (99); the quadrOpole-dipole interaction between the ferrocene (Fc) molecule and the solvent di- poles (102); and variations in the specific solvation of the ferricinium cation between solvents which are not entirely compensated by corresponding changes in the solva- tion of the ferrocene molecule (96,99). There are other indications of the inadequacy of the ferrocene assumption in the literature. Sahami and Weaver (103) determined the reaction entropy of Fc+/Fc redox couple in several solvents. The results indicated that in contrast to the Born estimates (Asgc)Born’ which were uniformly small and positive (1-6 e.u.), the experimental reaction entropies 71 increased markedly from a small negative value in water (-5 e.u.) to substantial positive values (ll-1A e.u.) in several dipolar aprotic solvents. These results clearly indicate that there are significant differences in the nature and extent of solvent polarization between fer- ricinium and ferrocene that are sensitive to the micro- scopic solvent structure. There is a more reliable extrathermodynamic method, the so-Called "tetraphenylarsonium-tetraphenylborate" (TATB) assumption (9A,98,lOO,lOl,lOA-106). This method is based on the assertion that the transfer free energies for PhuAs+ and PhuB- are equal; ELSL: AG;(phuAs+) = acg(phuB-) a 1/2 AG%(PhuAsPhuB). Nevertheless the ferrocene assumption can still provide a straightforward route to the evaluation of liquid Junction potentials in different solvents and therefore to the free energies of transfer on the TATB. scale, if the appropriate values of free energy of transfer for Fc+/Fc itself on this scale are known. Fortunately, the required values of free energies of transfer for Fe from water to most solvents can be easily obtained from the differences in the experimental values of the free energy of transfer for a given ion such as silver that have been obtained using the ferrocene and TATB assumptions (9A). Therefore the free energies of transfer for a given redox couple can be obtained from the following equation: )S‘w + A(AG° 5’“ (8) A(AGrc) FA(Ef r0 FC 72 W where A(E§C)S- is the change in formal potential for the redox couple of interest vs Fc+/Fc resulting from substi- tuting another solvent for water, MAG;c 23w, energy of transfer for Fc+/Fc from water to the same sol- is the free vent vs TATB. B. Determination of Reaction Entropies for Redox Couples Considering the general reaction: IIIL + e- (metal electrode) I MIIL (9) M X X II the reaction entropy AS;c of M ILx/MIILx redox couple can ’,be written as 03-0 _- =- -- ASrc Sred 86x 8&1 SIII (10) where SE1 and SE11 are the absolute ionic entropies of species MIILx (reduced) and MIII Lx (oxidized), respectively. Reaction (9) is only a half of a complete electrochemical cell reaction. As a result, any determination of the As;c for this reaction must involve some kind of extra- thermodynamic assumption. The most convenient method for the present study involves the use of nonisothermal electro- chemical cells (107,108). This is basically an electro- chemical cell in which the reference and working compart- ments are maintained at different temperatures. One 73 nonisothermal arrangement which was frequently employed in the present work can be written as: Pt, SCE(aq)||0.lM TEAP(sol.S)I0.lM TEAP(S), MIII-Mlll Hg or C A B C In the above arrangements, the reference electrode (SCE) was held at room temperature and the temperature of the working compartment BC was varied; the thermal liquid Junc- tion (109) was formed within the region AB so that the un- known solvent liquid junction potential at A did not affect the temperature dependence of formal potential. The formal potential Ef across nonisothermal cell was determined as a function of temperature. The temperature dependence of the formal potential can be separated into three components (109) m dEf _ d¢t2j + dOtC + d¢f (11) d ‘- dT dT dT where ¢t23 is the Galvani potential difference across the thermal liquid junction within the region AB, etc is the "thermocouple" potential difference between the hot and m f 18 the cold sections of the working electrode, and o 7A Galvani metal-solution potential at the working electrode. The important quantity in the present content is d®?/dT since: _ m A819,C - F(d¢f/dT) (12) Therefore one can obtain A830 values from measurements of the formal potential if the temperature coefficients of T and T are known or can be estimated. tic tc Absolute values of the Thomsen coefficient (dotc/dT) are known for several metals and are usually found to be on the order of a few microvolts per degree (109). Since the experimental values of dEf/dT are usually 1-2 mV/deg, it is clear that the contribution of the Thomson coef- ficient to the temperature coefficient of Ef is neg- ligible. Relative values of d¢tlj/dT are also known to be negligible with respect to dEf/dT (109). Therefore to a very good approximation (dEf/dT) = (deg/dT) so that dEf Asgc = F(Efif) (13) It is interesting to note that the values of A830 obtained in this study are essentially independent (within the experimental reproducibility of :1 e.u.) of the ionic strength u in the region of 0.1 i u i 0.5 M. This supports the assumption used here for the determination of reaction 75 entropies. The values of reaction entropies As;C can be used for determining the difference in the entropies of complexa- tion between the divalent (reduced) and trivalent (oxi- d d ci S° - ° ize ) spe es (A II,L ASIII,L) from III/II III/II L-S O — O = O _ O = O ASrC(MLx ) ASrC(M ) ASII,L ASIII,L A(AS ) (1n) III/II , III/II , where ASrc(M ) and ASrc(MLx ) are the reaction en- tropies for the corresponding solvated and complexed redox couples, respectively. The values of reaction entropies can also be used to determine the entropy of transfer of a redox couple from water to a nonaqueous solvent: 0 - o z 0 — O ASrc(solvent) ASrc(water) ASII,s-w ASIII,s-w = a(AS;C)S‘W (15) where ASSC (solvent) and A8?0 (water) are the reaction entropies for the corresponding solvated and aquo redox couple,respectively. CHAPTER V ELECTROCHEMICAL STUDIES OF SOME TRANSITION .METAL ION CRYPTATES IN VARIOUS SOLVENTS 76 A. Introduction Variations in the ligand and solvent medium are ex- pected to have large influences upon the thermodynamics and kinetics of electron transfer reactions. Part of these ef- fects can arise from changes in the composition of the co- ordination shell of the reacting species as well as from reactant—solvent interactions ("inner shell" and "outer shell" effects, respectively). In order to distinguish between these two contributions, we have chosen to do a systematic study of ligand and solvent effects upon thermo- . dynamics of redox couples involving substitutionally inert transition metal ion cryptates, where the oxidized and reduced species of these redox couples are both stable. The following redox couples were studied in several solvents, such as water, dimethylsulfoxide, N,N-dimethyl- formamide, N-methylformamide, formamide, propylene carbon- ate, and acetonitrile, (MC221)3+/2+, (M0222)3+/2+ (where M + Eu, Yb, Sm), (EuC2N22)3+/2+, (Fe0211)3+/2+, and 2+/+ (CuL) where L = C211, C2 11, C2 1 ). These solvents N NlN N were chosen because of two reasons: 1) They have rela- tively large dielectric constants (e > 35) which mini- mizes the solution resistance (ohmic drop), and prevents the extent of ion association in-the bulk solution. 77 78 2) The values of the dielectric constant,donor number, ac- ceptor number, and dipole moment of these solvents vary over a wide range (see Table 6), which should allow the effects of such factors on the thermodynamics of electron transfer to be explored systematically. Electrochemical studies of these redox couples in various solvents can help us to reach a better understand- ing of the various factors involved in the cryptate forma- tion, as well as the effect of ligand and solvent on the thermodynamics of electron transfer reactions. B. Results 1. M(III/II) Cryptate Redox Couples 1.1. Complexation Thermodynamics - Cathodic-anodic cyclic voltammograms were obtained for each of the tri- valent cryptates. Substantial changes in the electro- chemical behavior of the Eu3+/2+, Yb3+/2+, Sm3+/2+ Fe3+/2+ , and couples are found when these ions are encapsulated within cryptate cavities. The separation between the cathodic and anodic peak potentials for the solvated Eu, Yb, Sm, and Fe redox couples in 0.1 M TEAP (tetraethyl- ammonium perchlorate) is large and sweep rate dependent in some of the solvents studied here (see Table 7) re- flecting the slow heterogeneous electron-transfer kin- etics (110). On the other hand, the corresponding 79 .00000 m Oflmhmh 0m EOeHh HI 008.000x :0 009552 00:09 ccmsuso .Am00v cocoaomom 5000 009532 poudooo< camEpsoo n .0300V mocopomom 5090 00209 :0 020505 o00d0am m.:m m0, m.m0 mw.0 0mm 00003 0000 0.00 0.00 00.0 00000000 000200 00000000000000200 0.00 0.00 0.00 00.0 00002000 00:00 000E0eso000000s00-z.2 0.00 000 00.0 00002000 00:20 000202000000002-2 0.00 00 0.000 00.0 02000 000 000505000 0.00 00 0.00 0.0 00000 000020 00000002 \m 0 ,0 0.00 0.00 0.00 00.0 0000w0mw .0000 000000000 000000000 m.m0 0.:0 0.0m 0:.m zommo 000000coumo< 009832 009832 pnmpmcoo 0:080: manuosmum pco>0om chowdmoo< phonon o0nuoo0mHQ mo0oa0m .muzo>0om mso0pm> mo mo0uan00m 050m .0 o0nme 80 Table 7. Peak Separations of a Number of Redox Couples in Various Solvents Using 0.1 M TEAP as Supporting Electrolyte at 25°C. Sweep Peak . Rate Separation a Redox Couple Solvent (mV/sec) (mV) Electrode Eu3+/2+ H20 100 line Hg DMSO 200 70 Hg DMSO 50 .70 Hg DMF 100 70 Hg NMF 50 110 Hg F 100 175 He PC 50 150 Hg AN 200 150 Hg AN 100 130 Hg AN 50 125 Hg EuC2213+/2+ H20 50-500 65C Hg DMSO 50 62 Hg DMSO 200 65 Hg DMF 200 67 Hg NMF 50 65 Hg F 100 63- Hg PC 100 65 Hg PC 50 65 Hg AN 200 72 Hg AN 50 7o Hg EuC2223+/2+ H20 50-500 65C Hg DMSO 100 68 - Pt DMF 200 70 Hg DMF 50 7o ' Hg NMF 5O 70 Hg P 50 77 HS Table 7. Continued. 81 Sweep Peak . Rate Separation a Redox Couple Solvent (mV/sec) (mV) Electrode EuC2223+/2+ PC 200 70 Hg PC 100 .70 Hg AN 100 68 Hg AN 50 68 Hg EuczN223*/2+ H20 100 70 Hg H20 50 70 H8 DMSO 200 77 Hg NMF 100 76 Hg NMF 50 75 Hg F 100 75 Hg F 50 75 Hg Yb3+/2+ DMSO 50 75 Hg DMF 100 80 Hg NMF 100 80 Hg F 50 80 Hg PC 200 150 Hg ' PC 100 130 Hg AN 100 185 Hg YbC2213+/2+ H20 50—500C 65 Hg DMSO 100 65 Hg DMF 100 65 Hg NMF 50 65 Hg F 100 65 Hg PC 200 75 Hg AN 100 75 Hg Table 7. Continued. 82 Sweep Peak Rate Separation Redox Couple Solvent (mV/sec) (mV) Electrodea ch2223*/2+ DMSO 50 7o Hg DMF 100 65 Hg NMF 100 70 Hg F 100 75 Hz PC 50 70 Hg AN 100 75 H8 Sm3+/2+ DMSO 50 85 Hg DMF 100 65 Hg PC 100 150 Hg AN 100 1A0 Hg 3002213.”2+ DMSO 100 70 Hg DMF 100 65 Hg PC 100 75 Hg AN 100 75 Hg SmC2223+/2+ DMSO 200 75 He DMSO 50 73 He DMF 50 70 H8 PC 100 75 H8 AN 100 75 Hg Fe3+/2+ DMSO 100 70 Pt DMSO 50 70 Pt DMF 200 65 Pt DMF 100 65 Pt DMF 50 65 Pt NMF 50 150 Pt 17002113“2+ DMSO 100 70 Pt Table 7. Continued. 83 Sweep Peak Rate Separation Redox Couple Solvent (mV/sec) (mV) Electrodea FeC2ll3+/2+ DMSO 50 70 Pt DMF 100 70 Pt NMF 50 120 Pt 002V+ DMSO 200 250 C DMSO 50 195 C AN 100 250 Pt CuC2112+/+ H20 100 85 Hg DMSO 50 77 Hs DMF 100 86 Pt PC 100 90 Pt AN 100 92 Pt CuCZN112+/+ H20 50 110 Pt DMSO 100 68 Pt DMSO 50 66 Pt DMF 100 85 Pt PC 50 93 Pt AN 200 79 C AN 100 77 C CuC2N1N1N2+/+ H20 50 95 0 DMSO 50 85 Pt DMF 50 95 Pt PC 50 100 Pt AN 50 80 C J — aHg = Hanging Mercury Drop Electrode; Pt = Platinum Flag Electrode; C = Glassy Carbon Electrode. pr = 7. 0Values obtained from Reference uh. 8H voltammograms for the cryptate complexes of these ions in 0.1 M TEAP in all the solvents studied, have a smaller peak separation, close to 65 mV (see Table 7), expected for electrochemically reversible, one electron couples at room temperature (111). The only exception here is FeC2113+/2+ redox couple in NMF, which has a peak separation of about 115 mV. Similar results were obtained for Eu and Yb redox couples in water by Weaver gt a1 (H3,Hu). They have con- cluded that the heterogeneous electron-transfer rate constants of the Eu cryptates are at least two orders of 3+/2+ a magnitude larger than those for Eu q . (The values of electrochemical charge-transfer rate constant estimated for 3+/2+ 1 aq m8 x 10.-5 cm s-l, respectively). The values of peak sepa- the Eu cryptate and Eu couples are %.01 cm s- and rations for uncomplexed and complexed Eu, Yb, Sm, and Fe redox couples in various solvents (Table 7) indicate that the heterogeneous electron-transfer rate becomes faster when a lanthanide ion is encapsulated within a cryptate cavity, while in the case of Fe, it does not change con- siderably. I . The formal potentials Ef for Eu, Yb, Sm, and Fe cryp- tates obtained from the mean of the cathodic and anodic peak potentials (112) were found to be markedly more posi- tive than for uncomplexed Eu, Yb, Sm, and Fe couples in solvents with relatively high basisity such as, water, dimethyl sulfoxide, N,N-dimethylformamide, N-methylformamide, 85 and formamide. The values of Ef, along with the reaction entropies A8; for complexed and uncomplexed Eu, Yb, Sm, c and Fe couples in several solvents, are summarized in Tables 8-11. Identical cyclic voltammograms were obtained for the cryptate couples in the absence and presence of added cryptand. Thus both the trivalent and divalent cryptates are substitutionally inert on the timescale of cyclic volt- ammetry. Solutions of some of the first row transition metal 3+/2+ ion (III/II) redox couples, such as V (in water), Cr3+/2+ (in water, DMSO, and DMF), Co3+/2+ 2+/+ 2 have also been studied in the presence as well as in the (in DMSO), and Mn3+/2+ (in DMSO) as well as UO (in DMSO and DMF) absence of cryptand ligands. The cyclic voltammograms of 2+/+ 02 of cryptands C211 and C222 respectively, indicate that, these metal ions and U redox couples in the presence none of these redox couples forms a complex with cryptand ligands. Thus Fe3+ and Fe2+ are the only first row transi— tion metal ions studied here, which can form complexes with C211 ligand in a number of solvents such as, DMSO, DMF, and NMF. It should be mentioned that in the presence of excess C211 only an anodic peak, due to the oxidation of 2+ FeC2ll to FeC21l3+ was observed, while, when the analytical concentration of the ligand is less than that of + Fe 2, both cathodic and anodic peaks were observed. This is probably due to the rapid dissociation of FeC2113+ 86 Table 8. Formal Potentials and Reaction Entropies for Eu3+/2+, (EuC221)3+/2+ 3+/2+ , (EuC222) , and (EZuC2N22)3+’2+ Redox Couples in Various Solvents at 25°C. Ionic Strength Eica Asgcb Redox Couple Solvent (M) (mV) (e.u.) Eu3+/2+ H2O 0.1 —7A8C’d A8C DMSO 0.1 -1278 A5 DMSO 0.5 -1321 A6 DMF 0.1 -1079 56 NMF 0.1 -12o8d 26 NMF o.A -1225d 26.5 F 0.1 -1025d 21.5 F 0.5 -1o37d 21.5 PC 0.1 - A88f AN 0.1 - 213f (EuC22l)3+/2+ H20 0.1 - 55oC H20 0.5 — 5600’e 27.5c DMSO 0.1 - 739 31 DMSO 0.5 - 775 32 DMF 0.1 - 660 35 NMF 0.1 - 7A5 23 NMF 0.A - 757 23.5 F 0.1 - 666 19.5 p 0.5 - 672 19.5 PC 0.1 - 511 3A AN 0.1 - 392 37.5 (EuC222)3+/2+ H20 0.1 - 33C0 21C DMSO 0.1 - 533 20 DMSO 0.5 - 569 20 DMF 0.1 — A27 29 87 Table 8. Continued. Ionic Strength Ego Asgcb Redox Couple Solvent (M) (mV) (e.u.) (EuC222)3+/2+ NMF 0.1 - 596 19.5 F 0.1 - 502 21 F 0.5 - 506 21.5 PC 0.1 - 2A3 32 AN , 0.1 - 222 26 (EuC2N22)3+/2+ H2O 0.1 - 5AA 19 DMSO 0.1 - 733 2A NMF 0.1 - 834 26 F 0.1 — 722 ‘j' 23 aFormal potential for redox couple in solvent given, using TEAP as supporting electrolyte unless otherwise noted; versus ferricinium/ferrocene couple in same electrolyte. Obtained using cyclic voltammetry. bReaction entropy of redox couple in listed solvent obtained from temperature dependence of Ef using nonisothermal cell. 0Obtained from Reference Mu. dNapTS was used as supporting electrolyte. eNaClOu was used as supporting electrolyte. fIn the case of relatively large peak separations (90-120 mV), the uncertainty of Ef is 5-10 mV. 88 Table 9. Formal Potentials and Entropies of Electron Trans- fer Reactions of Ytterbium Cryptate Redox Couples in Various Solvents at 25°C (Ionic Strength = 0.1 M). E§~°a as." Redox Couple Solvent (mV) (e.u.) Yb3+/2+ H2O —15A8 A8 DMSO V -1955 45 DMF -1768 52 NMF -1899 F -17A8 15 PC -1119° AN -1oA2c (YbC22l)3+/2+ H20 -1227 27.5 DMSO -1A15 25 DMF -1315 2A NMF -1391 15.5 F —1305 1A PC -1o93 38 AN -1036 53 (YbC222)3+/2+ DMSO -12A8 DMF -1110 29 NMF —126A 18 F —11A7 16 PC - 978 A5 AN — 95A “3 aFormal potential for redox couple in solvent given, using TEAP as supporting electrolyte; versus ferricinium/ferro- cene couple in same electrolyte. Obtained using cyclic voltammetry. bReaction entropy of redox couple in listed solvent obtained from temperature dependence of Ef using nonisothermal cell. 0In the case of relatively large peak separations (90- 120 mV) the uncertainty of Ef is 5-10 mV. 89 Table 10. Formal Potentials and Entropies of Electron Trans- fer Reactions of Sm3+/2+, (Sm0221)3+/2+, and (SmC222)3+/2+ Redox Couples in 0.1M TEAP in Various Solvents at 25°C. EFca AS° b f rc Redox Couple Solvent (mV) (e.u.) 30372+ DMSO -2A73 DMF -2237 59 PCc -15A3 ANc -1361 (SmC22l)3+/2+ DMSO -196A DMF -1823 29 PC -16AO 28 AN —1579‘ 25.5 (SmC222)3+/2+ DMSO -176o DMF -1623 39.5 PC -1AA8 33.5 AN -1A28 28 aThe values of formal potentials are reported versus fer- ricinium/ferrocene couple. bReaction entrOpy of redox couple in listed solvent ob- tained from temperature dependence of Ef using noniso- thermal cell. 0The undertainty of Ef is 5010 mV. 90 Table 11. Formal Potentials and Entropies of Electron Trans- fer Reactions of Fe3+/2+ and (FeC2ll)3+/2+ Redox Couples in 0.1M TEAP in Various Solvents at 25°C. a EEC Asgcb Redox Couple - Solvent (mV) (e.u.) Fe3+/2+ DMSO -200 33.5 DMF — A5 ' 28 NMFc -335 (FeC211)3+/2+ DMSO 10A 26 DMF 1A8 28 NMFc 18o aThe values of formal potentials are reported versus fer- ricinium/ferrocene couple. bReaction entropy of redox couple in listed solvent ob- tained from temperature dependence of Ef using nonisothermal cell. 0The uncertainty of Ef is 5-10 mV. 91 in the presence of excess C2ll ligand. As mentioned in Chapter IV, the difference in formal potentials Ef between the complexed and uncomplexed one- electron redox couples is related directly to the difference in the free energies of complexation for the trivalent and divalent cryptates (Equation 5 from Chapter IV)., The )L-S resulting values of -A(AG° [i.e., or (AG° - AG° III,L II,L)] are listed in Tables 12-15. It is seen that the stabilities of the trivalent cryp- tates are substantially smaller than those of the correspond- ing divalent cryptates in a number of solvents; i.e., the values of (AGEII L - AG ) are large and positive. In 3 O II,L order to ascertain the factors responsible for this be- havior,.it is desirable to evaluate the enthalpic and en- tropic contributions to (AGEII L - AG The differences 9 o ). II,L between the complexation entropies of trivalent and di- valent cryptates can be determined using Equation 1“ from Chapter IV. The values of -A(AS°)E""S [i.e., or (ASEII L _ ’ AS° )] in various solvents are given in Tables 12-15]. II,L It is shown that these values are also positive. Therefore ‘ o _ o the large positive values of (AGIII,L AGII,L) [i.e., -A(AG°)L-S] are associated with still larger values of the o _ 0 corresponding enthalpic terms (AHIII,L AHII,L) [i.e., -A(AH°)L-S] (see Tables 12-15). 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